Questions tagged [integrable-systems]
110 questions
2
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0 answers
Why is it important to study Lax pair in integrable system?
I know that once we find the Lax pair $\dot{L}=[L,M]$ we could get the conserve quantities $H_k = \frac{1}{k}{\rm Tr}L^k$. But it seems that there is not general way to construct the Lax pair (e.g. in How to find a lax pair of an integrable system…
Black Monolith
- 131
- 3
2
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How to find Backlund transformation between the KdV and mKdV equations?
Starting with the Miura transformation $v_x = - u -v^2$, how can I find the other half to the backlund transformation which will take solution of the KdV $u_t + 6 u u_x +u _{xxx}$ to a solution of the mKdV $v_t - 6 v^2 v_x +v_{xxx}$?
The unknown…
User
- 309
0
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0 answers
bi-Hamiltonian structure of the Sine-Gordon equation
It is well known that the sine-Gordon equation in laboratory (or light-cone) coordinates,
\begin{align}
\ddot\phi-\phi''=\sin\phi,\\
\dot\varphi'=\sin\varphi,
\end{align}
respectively, is an integrable system [1]. However, I have been searching in…
hyriusen
- 117
0
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there seems to be a statement that is provable in integrable system, please let me know where can I learn about this statement.
the statement is:
given $f,g \in C^{\infty}(M)$ the it's true that $\xi_{\{f,g\}}=[\xi_{f},\xi_{g}]$
M should be a symplectic poisson manifold
kristenA
- 1
0
votes
1 answer
Prove that $\int g\ {\rm d} \mu<\infty$?
Let $(S,\mathcal{A},\mu)$ be aprobability space and $g\ge 0$ with $\int g\ln^+\ln^+ g {\rm d} \mu<\infty$. Can you help me prove that $\int g\ {\rm d} \mu<\infty$?
LeeWoo
- 143